.TH std::acos(std::complex) 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::acos(std::complex) \- std::acos(std::complex)

.SH Synopsis
   Defined in header <complex>
   template< class T >                      \fI(since C++11)\fP
   complex<T> acos( const complex<T>& z );

   Computes complex arc cosine of a complex value z. Branch cuts exist outside the
   interval [−1, +1] along the real axis.

.SH Parameters

   z - complex value

.SH Return value

   If no errors occur, complex arc cosine of z is returned, in the range of a strip
   unbounded along the imaginary axis and in the interval [0, +π] along the real axis.

   Error handling and special values

   Errors are reported consistent with math_errhandling.

   If the implementation supports IEEE floating-point arithmetic,

     * std::acos(std::conj(z)) == std::conj(std::acos(z))
     * If z is (±0,+0), the result is (π/2,-0)
     * If z is (±0,NaN), the result is (π/2,NaN)
     * If z is (x,+∞) (for any finite x), the result is (π/2,-∞)
     * If z is (x,NaN) (for any nonzero finite x), the result is (NaN,NaN) and
       FE_INVALID may be raised.
     * If z is (-∞,y) (for any positive finite y), the result is (π,-∞)
     * If z is (+∞,y) (for any positive finite y), the result is (+0,-∞)
     * If z is (-∞,+∞), the result is (3π/4,-∞)
     * If z is (+∞,+∞), the result is (π/4,-∞)
     * If z is (±∞,NaN), the result is (NaN,±∞) (the sign of the imaginary part is
       unspecified)
     * If z is (NaN,y) (for any finite y), the result is (NaN,NaN) and FE_INVALID may
       be raised
     * If z is (NaN,+∞), the result is (NaN,-∞)
     * If z is (NaN,NaN), the result is (NaN,NaN)

.SH Notes

   Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut
   on the complex plane. The branch cut is conventionally placed at the line segments
   (-∞,-1) and (1,∞) of the real axis.

   The mathematical definition of the principal value of arc cosine is acos z =

   1
   2

   π + iln(iz +
   √
   1-z2
   ).

   For any z, acos(z) = π - acos(-z).

.SH Example


// Run this code

 #include <cmath>
 #include <complex>
 #include <iostream>

 int main()
 {
     std::cout << std::fixed;
     std::complex<double> z1(-2.0, 0.0);
     std::cout << "acos" << z1 << " = " << std::acos(z1) << '\\n';

     std::complex<double> z2(-2.0, -0.0);
     std::cout << "acos" << z2 << " (the other side of the cut) = "
               << std::acos(z2) << '\\n';

     // for any z, acos(z) = pi - acos(-z)
     const double pi = std::acos(-1);
     std::complex<double> z3 = pi - std::acos(z2);
     std::cout << "cos(pi - acos" << z2 << ") = " << std::cos(z3) << '\\n';
 }

.SH Output:

 acos(-2.000000,0.000000) = (3.141593,-1.316958)
 acos(-2.000000,-0.000000) (the other side of the cut) = (3.141593,1.316958)
 cos(pi - acos(-2.000000,-0.000000)) = (2.000000,0.000000)

.SH See also

   asin(std::complex)  computes arc sine of a complex number
   \fI(C++11)\fP             (\\({\\small\\arcsin{z}}\\)arcsin(z))
                       \fI(function template)\fP
   atan(std::complex)  computes arc tangent of a complex number
   \fI(C++11)\fP             (\\({\\small\\arctan{z}}\\)arctan(z))
                       \fI(function template)\fP
   cos(std::complex)   computes cosine of a complex number (\\({\\small\\cos{z}}\\)cos(z))
                       \fI(function template)\fP
   acos
   acosf               computes arc cosine (\\({\\small\\arccos{x}}\\)arccos(x))
   acosl               \fI(function)\fP
   \fI(C++11)\fP
   \fI(C++11)\fP
   acos(std::valarray) applies the function std::acos to each element of valarray
                       \fI(function template)\fP
   C documentation for
   cacos
